Molecule Types Symmetric Tops | <Prev Next> |
There is one of these for each perturbation parameter in each state. There are many possible perturbation types, as described below. To see the actual matrix elements used in any particular case, right click on the perturbation and select "Matrix Elements". The resulting expressions will be displayed in the log window, and should be understood as being multiplied by the Value parameter.
Note that if degenerate states are involved, careful selection
of the lPower and lChange values
will be required. For example, the common A1 - E
Coriolis interaction requires pPower = 1, lPower
= -1 and lChange = 1. If the combination of values are
set wrong, the resulting matrix element will typically be zero,
or give an error message about a symmetry mismatch.
Nucleus | Index, starting from 1, of nuclear spin involved in perturbation; 0 (default) for those not involving a nuclear spin. |
SymSelect | Symmetry select |
ScalePrev | Scale factor with respect to preceding perturbation |
JPower | Twice power of N2 = N(N+1) (= J(J+1)
for closed shell systems with S = 0). |
zPower | Power of Nz; If both zPower and pPower are non zero
then the effective operator is either: NJPower/2[Nz|zPower|, N+|pPower|+N-|pPower|]+
or NJPower/2[Nz|zPower|-1,[Nz, N+|pPower|+N-|pPower|]+]+ if zPower is odd and < -2 |
pPower | Power of N± |
lPower | Select l
dependence; valid values are 0 (l independent), 1 or -1. If lChange is 0, the
matrix element is multiplied by l*lPower,
otherwise the matrix element is multiplied by sign(l'-l)*lPower. |
lChange | Power of l+ or l-; < 0 implies opposite sign to change in K; valid values are -2..2 |
KSelect | K the perturbation applies to |
SPower | Twice power of S2 = S(S+1) |
SzPower | Power of Sz.
If this is combined with a rotational operator, the overall
operator is:[NJPower/2[Nz|zPower|, N+|pPower|+N-|pPower|]+,SzSzPower]+ |
SpPower | Power of S±.
If this is combined with a rotational operator, the overall
operator is (if pPower and SpPower have
the same sign):[NJPower/2[Nz|zPower|,N+|pPower|]+, S+|SpPower|]+ + [NJPower/2[Nz|zPower|,N-|pPower|]+, S-|SpPower|]+If pPower and SpPower have opposite signs: [NJPower/2[Nz|zPower|,N+|pPower|]+, S-|SpPower|]+ + [NJPower/2[Nz|zPower|,N-|pPower|]+, S+|SpPower|]+ |
NSPower | Power of N.S. |
Value | Size of perturbation; the expressions and operators given here should be understood to be multiplied by this. |
Operator |
JPower |
zPower |
pPower |
lPower |
lChange |
Scale Factor |
Notes |
|
B | N2 | 2 |
0 | 0 |
0 | 0 | 1 |
Both terms required to replicate B[J(J+1) - K2] |
Nz2 | 0 |
2 |
0 |
0 |
0 |
-1 |
||
C | Nz2 | 0 | 2 | 0 | 0 |
0 | 1 |
|
DJ | N4 ≡ N2(N+1)2 | 4 | 0 | 0 | 0 | 0 | -1 | |
DJK | N2Nz2 ≡ N(N+1)K2 | 2 | 2 |
0 | 0 | 0 | -1 | |
DK | Nz4≡ K4 | 0 | 4 |
0 | 0 | 0 | -1 | |
zeta |
Nzlz | 0 |
1 |
0 |
1 |
0 |
-2C |
In this form, parameter must be -2Cζ, not -2ζ |
etaJ |
N2Nzlz | 2 |
1 |
0 |
1 |
0 |
1 |
|
etaK |
Nz3lz | 0 |
3 |
0 |
1 |
0 |
1 |
|
qplus |
N+2l+2+N-2l-2 | 0 |
0 |
2 |
0 |
2 |
½ |
|
qminus |
N+2l-2+N-2l+2 | 0 |
0 |
2 |
0 |
-2 |
½ | |
r |
[N+l-2+N-l+2,Nz]+ | 0 |
1 |
1 |
0 |
-2 |
1 |
|
DqJ |
N2(N+2l+2+N-2l-2) | 2 |
0 |
2 |
0 |
2 |
½ | |
DqK |
[N+2l+2+N-2l-2,Nz2]+ | 0 |
2 |
2 |
0 |
2 |
½ | |
DrJ |
N2[N+l-2+N-l+2,Nz]+ | 0 |
1 |
1 |
0 |
-2 |
1 |
|
DrK |
[[N+l-2+N-l+2,Nz]+,Nz2]+ | 0 |
-3 |
1 |
0 |
-2 |
1 |
zPower <= -3 flags use of two
anticommutators |
HJ | N6 | 6 | 0 | 0 | 0 | 0 | 1 |
|
HJK | N4Nz2 | 4 | 2 |
0 | 0 | 0 | 1 |
|
HKJ | N2Nz4 | 2 | 4 |
0 | 0 | 0 | 1 |
|
HK | Nz6 | 0 | 6 |
0 | 0 | 0 | 1 |
|
LJ | N8 | 8 | 0 | 0 | 0 | 0 | 1 |
|
LJJK | N6Nz2 | 6 | 0 | 0 | 0 | 0 | 1 |
|
LJK | N4Nz4 | 4 | 0 | 0 | 0 | 0 | 1 |
|
LKKJ | N2Nz6 | 2 | 0 | 0 | 0 | 0 | 1 |
|
LK | Nz8 | 0 | 0 | 0 | 0 | 0 | 1 |
Operator |
JPower |
zPower |
pPower |
lPower |
lChange | SzPower |
SpPower |
SPower |
NSPower |
Scale Factor |
|
ebb | N+S- + S+N-+
N-S+ + S-N+ = 2(N+S- + N-S+) = 8(NxSx+NySy) |
0 |
0 |
1 |
0 |
0 |
0 |
-1 |
0 |
0 |
1/4 |
ecc |
NzSz + SzNz
=2NzSz |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
½ |
DsN | N2N.S | 2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
DsNK |
[N2, NzSz]+ | 2 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
½ |
DsKN |
N.S Nz2 | 0 |
2 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
DsK |
[Nz3, Sz]+
= 2Nz3Sz |
0 |
3 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
½ |
alpha |
Sz2 | 0 |
0 |
0 |
0 |
0 |
2 |
0 |
0 |
0 |
3 |
S2 | 0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
0 |
-1 |
|
beta |
S+2-S-2 | 0 |
0 |
0 |
0 |
0 |
0 |
2 |
0 |
0 |
½ |
aeff |
lzSz | 0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |